Question

A total of 55 chocolates were distributed among 13 children such that each girl gets 3 chocolates and each boy gets 5 chocolates. Which of the following is the number of girls?
A) 8
B) 3
C) 4
D) 5

Answer 1

Answer:

D

Step-by-step explanation:

Let the

number of girls be x,

and number of boys be y

according to question:

x + y = 13 [let this be eq 1]

3x + 5y =55 [let this be eq 2]

solving eq 1 and 2 by subtraction method:

3x + 5y = 55

x + y = 13

____________

2x + 4y = 42

2x = 42 - 4y

x = 21 - 2y

now,

putting the value of x in eq 1:

x + y = 13

21 - 2y + y = 13

- y = - 8

therefore,

y = 8

putting value of y in eq 1

x + y = 13

x + 8 = 13

therefore x = 5

hence the number of girls is 5.

Answer 2

Given:

A total of 55 chocolates were distributed among 13 children such that each girl gets 3 chocolates and each boy gets 5 chocolates.

To Find:

Which of the following is the number of girls?

Solution:

according to question,

x + y = 13                        [eq 1]

3x + 5y =55                    [ eq 2]

solving eq 1 and 2 by subtraction method:

3x + 5y = 55

x + y = 13

2x + 4y = 42

2x = 42 - 4y

x = 21 - 2y

now,

putting the value of x in eq 1, we get

x + y = 13

21 - 2y + y = 13

- y = - 8

y = 8

putting value of y in eq 1

x + y = 13

x + 8 = 13

x = 5

Hence, the number of girls were 5 (option D).